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SUMMARY:A New Formulation of Analytic\, Non-Perturbative\, Gauge-and Loren
tz-Invariant QCD
DTSTART;VALUE=DATE-TIME:20110809T185000Z
DTEND;VALUE=DATE-TIME:20110809T191000Z
DTSTAMP;VALUE=DATE-TIME:20210119T132023Z
UID:indico-contribution-1350996@indico.cern.ch
DESCRIPTION:Speakers: Herbert Fried (Brown University)\nA simple and previ
ously overlooked choice of one parameter allows the Schwinger/Symanzik Gen
erating Functional of QCD to be re-written in a manifestly gauge-invariant
fashion\, without the need of Fadeev-Popov insertions. When combined with
Fradkin functional representations for the Green's function\, G[A]\, of a
quark in an effective color potential A\, and the vacuum loop functional
L[A]\, all QCD correlation functions can be represented as Gaussian\, func
tional-linkage operations connecting relevant combinations of G[A] and L[A
]. And because the Fradkin representations for those functionals are Gauss
ian in their dependence on A\, the functional-linkage operation can be don
e exactly\, and one then sees that gauge invariance here is achieved by ga
uge-independence\, as the gauge-dependent gluon propagators exactly cancel
out everywhere. In this way\, the non-perturbative sums over Feynman grap
hs reduce to an explicit\, gauge-independent functional expression.\n\n
That new\, final functional expression now displays a new property we ca
ll "Effective Locality" (EL)\, in which the infinite sum over infinite cla
sses of Feynman graphs corresponds to the exchange of a well-defined "gluo
n bundle" from specific space-time points on interacting quarks and/or ant
iquarks. And one then sees that it is no longer possible to continue to tr
eat quarks as ordinary particles\, with well defined asymptotic momenta or
positions\, for they are bound objects whose transverse coordinates can n
ever be measured exactly. Once this necessity of introducing realistic "tr
ansverse imprecision" is realized\, and introduced into the fundamental La
grangian\, all functional sums become well-defined\, and one has an analyt
ic way of obtaining physical information.\n\n It should be noted that
such progress is possible because the Fradkin representations are Potentia
l Theory constructs\, with reasonable approximations in different physical
situations\; e.g.\, at high energies\, G[A] simplifies to a Bloch-Nordsie
ck/eikonal form. With those simplifications\, and the remarkable property
of EL\, we have been able to calculate eikonal amplitudes for quark-antiqu
ark scattering\, and for three-quark scattering\, and to extract from thes
e eikonal functions the form of binding potentials that produce hadrons. A
nd\, most interesting\, for the first time we can exhibit a mechanism whic
h leads to effective Yukawa scattering between nucleons\, including a scat
tering potential which becomes negative\, as needed to make a deuteron fro
m a proton and a neutron. This\, to our knowledge\, and for the first time
ever\, is Nuclear Physics from basic\, realistic QCD.\n\n This work\,
by myself (HMF)\, French colleagues Grandou and Gabellini (of the Univers
ite de Nice)\, and my ex-Brown student Ming Sheu\, is barely 18 months old
at this writing\; and there are many problems remaining to be studied\, s
uch as non-perturbative renormalization theory\, the quark-gluon plasma\,
and - indeed - all of Nuclear Physics. On the basis of what we have been a
ble to derive up to this point\, we believe that this approach to analytic
QCD calculations will\, in the future\, become extremely useful. It shoul
d be noted that the above remarks are a description of "textbook" QCD\, wi
th one type of quark and the massless gluons of SU(3)\; flavors and electr
oweak effects\, as well as spin and angular momentum dependences are to be
added in later on.\n\nhttps://indico.cern.ch/event/129980/contributions/1
350996/
LOCATION:Rhode Island Convention Center 551 A
URL:https://indico.cern.ch/event/129980/contributions/1350996/
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